General Model for Unsaturated Hydraulic Conductivity for Soils with Lognormal Pore‐Size Distribution

Abstract

Abstract Describing water flow in unsaturated soils requires knowledge of the unsaturated hydraulic conductivity. This study was conducted to develop a general conductivity model for soils with lognormal pore‐size distribution based on the Mualem‐Dagan pore‐scale model. The derived model has three parameters other than parameters for a retention model: the parameters α and β, both of which are related to the soil pore tortuosity, and the parameter γ to describe how to evaluate the effective pore radius. The proposed model was applied to observed retention and conductivity data sets for 200 soils. Results showed that both α and β should be treated as fitted parameters for accurate descriptions of conductivity, whereas estimation results were insensitive to γ as long as α and β were optimized. Consequently, a simplified form of the general conductivity model was suggested which uses the constant γ value of unity. Based on the simplified general conductivity model, two predictive methods (AB and FN) were developed. The method AB uses the constant α and β values to minimize the average prediction error. The method FN uses an empirically derived relationship between β and the dimensionless parameter of the retention model, and the constant α value to minimize the average prediction error. Both methods reduced the average prediction error more than 77% compared with the Burdine and Mualem predictive models. The method FN provided slightly better predictions than the method AB, reducing the average prediction error by 28%.